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The distribution of totients

By Kevin Ford

Abstract

New version of my 1998 article. The method of proof of the main results follows the original, but there are many simplifications/streamlining of arguments, especially Lemma 3.6 (new Lemma 3.7). Fixed small error in proof of lower bound for V_k(x) (see the paragraph after (5.20)), fixed the statement and proof of Theorem 3. New, precise way to relate sums to volumes (Lemmas 3.1, 3.9) and provided full details in Section 6 of the proofs of Theorems 10-13. Slightly different versions of Theorems 10,11,12,14 (qualitatively the same) with simpler proofs. Sections 7 and 8 combined (new section 7). A few definitions, such as S-normal, changed slightly. Some reorganization of material.Comment: very minor revision: Corrected statement of Lemma 7.2 and following comment

Topics: Mathematics - Number Theory
Year: 2013
OAI identifier: oai:arXiv.org:1104.3264
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